Finding the coefficient of determination and the explained variation

Intro

Howdy!  I’m Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we’re going to learn how to find the coefficient of determination and the explained variation.  Here’s our problem statement: Use the value of the linear correlation coefficient R to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Part 1

OK, so the first part asks us for R-squared.  Even if you don’t know what the coefficient of determination is, you can get the value that you need to put in the answer field just by noticing they give you a value here for R and they’re asking for R-squared.  So all we have to do is square this value for R, and that gives us the coefficient of determination.

So let’s get out our calculator, and I’ll put in the value there for R, square it, and I’m asked to round to four decimal places.  Excellent!

Part 2

And now the second part of the problem asks for “the percentage of the total variation that can be explained by the linear relationship between the two variables.”  This is the explained variation.  And the explained variation is exactly the same as the coefficient of determination; the two are identical.

So all I have to do is take this number here that I’ve already calculated in the first part and notice that it wants it in percent form.  So I just take that number and put it in percent form.  Good job!

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